The following is an answer and/or comment by inhahe aka ColorStorm (inhahe.com - myriachromat.wordpress.com).
Good question, I think about this often. I'm not entirely sure, but I have a few ideas.

1. We already look up to people more who are more popular, I guess that's just the way humans are built. Is it some evolutionary-psychological mechanism in effect, or is it something that stems from other, more intuitively understandable psychological principles? Either way, celebrities are ridiculously, over-the-top popular. Where a normal popular person is known or liked by dozens of people, a celebrity is known or liked by literally millions if not billions. So, using some very simplistic reasoning, they'd be looked up to millions of times more than a regular person. This amounts to being worshiped.

2. Celebrities are celebrities precisely because they're extraordinary people. It's not necessarily just in our heads. Of all the possible candidates for being famous, which ones are going to win? Obviously the prettiest, or the brightest, or the ones with the most life and personality, etc. Something or another. So people like them because they have one or more qualities that people adore and they have them to extreme levels.

3. Celebrities appear larger than life to us, sometimes literally. They're on the TV, they're in the theater, they're on products, they're in the media and conversations, they're everywhere. It's like we're sitting there in a trance-like state staring wide-eyed and drooling at the screen for hours a day and there they appear. Injected hypnotically straight into the depths of our minds and into our appreciation of all things sensational. It's like when you see someone on TV that cements them into our reality on a totally different level. It makes them a God, because not just anybody can be on TV, you certaintly can't, and you know the same thing is showing in millions of homes and it's glowing brightly...

There's something about what appears on TV that's, I dunno, revered, for lack of a better word. Here's an example: When I was young and playing video games for basically the first time (Super Mario Brothers on the NES), the most thrilling thing for me wasn't even the fact of playing the game and exercising skill and exploring worlds, etc., it was that I could actually, with my own physical actions, *control* what happened on the TV. So just imagine what it means to us when a person is 'big' enough to able to appear on TV..

That's a good word for it, 'big', we see celebrities as somehow 'bigger' than everyone else. Just like in the phrase 'make it big'. That's why we care so much about every detail of their personal lives, or about being 'noticed' by them, etc. I saw a lady asking a guy a question on Twitter today about why he included a certain answer in a list of answers pertaining to a hashtag. I thought it was a little odd, she was an old lady and it wasn't phrased in a way hat made me think she was hitting on him or had a crush on him, or that they knew each other well, and it just seemed odd for someone to openly take that kind of an interest in someone for none of the above reasons. Then I noticed that the person she was asking was a celebrity. A very 'big' celebrity, Mark Hamill. Then it all made sense. But the juxtaposition between when it did make sense and when it didn't make sense allowed for some gaining of perspective regarding how people naturally regard and treat celebrities differently.

comment:
It also helps a little that actors are given scripts to for things to say, singers are put in the context of singing beautiful music, etc., so celebrities tend to appear more interesting than the average person and than they really are.